The human eyes are among the smallest organs in the entire body. They are, however, two of the most important organs to many people, since sight is the sense that humans tend to rely on most. While it's true that the human body is like one big machine and that nothing acts independently of anything else, there are remarkably few organs that act in direct concert with the eyes. The main organ that the eyes interact with is the brain, but they also interact with a variety of body systems such as the nervous system and the muscular system.
In order for people to see, there has to be light. Light enters the eye, which focuses the refracting light from the world and lets us perceive shape, color, distance, and so forth. The light is then transmitted by nerve signals along the optic nerve to the brain. In the human brain, the images that the eyes receive are interpreted and used to form an impression of the world around us. The visual cortex, the part of the brain that interprets sight, actually receives images upside down from both eyes, so it not only has to merge the pictures into a cohesive whole, but it also has to flip them right side up.
Organs and Systems
Obviously, the main organ that works with the eyes is the brain, specifically the visual cortex that interprets what it is that the eye is seeing. However, there are a number of organ systems that also work with the eye. The muscular system is connected to the eye since it's muscle tissue that allows the eye to turn and rotate in its socket. The nervous system is also linked to the eye in that the optic nerve transmits the impressions from the eye to the brain. The eyes are also linked to the vascular system, since they must be supplied with blood and nutrients to function, but the same can be said of any organ in the human body.